Is there any interest in using 0/1 instead of T/F in propositional logic?
Does it allow things the T/F notation doesn't?
Does it make easier or simplyfy in any way the exposition of logical theory?
I partially disagree with Arthur. If you are using $0/1$ instead of $T/F$. Then so long as you are in two valued logics then both are same for practical purposes.
However, using $0/1$ instead of $T/F$ has some other advantages. I will mention only two.
First, whenever you use $0/1$, a natural idea would be to extend this truth-value set to more than two values. The idea of having more than two values comes arguably more naturally if you are working with integers values than symbols.
Second, notice that whenever you use the notation $0/1$ , you immediately get a natural order between them. This is not so obvious in case of $T/F$. So this also naturally rises the question whether the "truth-value set" can be seen as a poset.
Changing the names of variables rarely affects anything. It may help you to think about what happens, but it doesn't change any formal properties.
Using $0$ and $1$ as truth values allows us to reduce logic to arithmetic. So if $t(P)$ is the $0/1$ truth value of proposition $P$ then
$t(\lnot P) = 1-t(P) \mod 2\\t(P \land Q) = t(P)t(Q) \mod 2 \\ t(P \oplus Q) = t(P) + t(Q) \mod 2\\t(P \lor Q) =t(P)+t(Q)+t(P)t(Q) \mod 2$
Then if we know that properties such as double negation, commutativity and associativity hold in the realm of arithmetic, we can immediately derive equivalent properties in the realm of logic.